ok... so im thinking about getting an arduino and i have one question: can it run a program w/o being connected to a computer? if so how easily. P.S. please excuse my spelling
Yes it can 
You need a computer to program it, but you can disconnect it from the computer completely after it's been programmed
You would just need a suitable power supply or battery to power it
All you need is something like this little adapter.
And maybe one of these since Alkaline 9V batteries don't last very long with the 25 mA load of the Arduino PCB. Fill this baby up with 6 AA rechargeable NiMH batteries and save yourself all kinds of money,
http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail?name=BH26AASF-ND
You may find this cable handy as well.
This is the 2.1 x 5.5 mm barrel power connector that most of the Arduino boards use. I'm sure there is a less expensive source someware but I haven't found one yet. this is a top quality connector made my Switchcraft.
Good luck and have fun.
KG2